We are going to talk about a two-dimensional model in statistical mechanics, the double-dimer model, which is simply a straightforward generalization of the dimer model. The latter is well-known in both physics and mathematics because of its particular features and substantial relations to many contexts, known in combinatorics as a perfect-matching problem. Here the emphasis is on the critical behavior of the loop ensembles of the double-dimer model, conjectured to converge to the level sets of the Gaussian free field and Schramm-Loewnerevolution or conformal loop ensembles with parameter 4. We use the Grassmannian representation of the dimer ...